Problem: Simplify the following expression: $a = \dfrac{7}{5k - 1} \div \dfrac{9}{10k}$
Explanation: Dividing by an expression is the same as multiplying by its inverse. $a = \dfrac{7}{5k - 1} \times \dfrac{10k}{9}$ When multiplying fractions, we multiply the numerators and the denominators. $a = \dfrac{ 7 \times 10k } { (5k - 1) \times 9}$ $a = \dfrac{70k}{45k - 9}$